Instrument for obtaining dynamically-symmetrical ratios



Jan. 27, 1931. F. ROBBINS ,7 ,0

INSTRUMENT FOR OBTAINING DYNAMICALLY SYMMETRICAL RATIOS Filed Oct. 10, 1925 Eg-Z z c D 2 U F19 J Y" Y 4 Inventor. I w f'iara' Robbins.

' B 9 71%M7 M/ v fTt tornega Patented Jan. 27.1931 6 nrnr n r.eres

rem) ROBBINS}. or MINNEAPOLIS, nirn'nnsorn, ASSIGNQE r0 roan noBBINs; V renewal), or MrminAro rs, MINNESOTA, A cosronnrron INSTRUMENT non on'reiiame DYNAMICALLYfiYEIMETRiCAL nnrros Application filed 'OctoberIO, 1925. Serial n 61,5369.

My invention relates to instruments for obtaining dynamically symmetrical ratios. Anobject'ofthe invention is to provide an instrument by means of which proportionally balanced space divisions intheir work may be r adily obtained by architects, en gi neers,'designe1s,' landscape ga'rdeners,- and all other draftsmen. Iaccomplished the objects' of my invention by providing an ini strument by means of which various rectangles may be laid off whose sides bear a square root relationship to their ends j and also by -1neans of which rectangles may be laid out in which the sides and ends have a ratio of 1.618 to 1. i

The full objects and advantages of my invention will appear in connection with the detailed description thereof and the novel.

features embodied in my inventive idea will be particularly pointed out in the claims.

F 1 is adiagrammatic View showing the manner of constructing a 1.618 rectangle. Fig. 2 is a plan view of a preferred form of the completedinstrument. Fig. 3 is a diagrammatic view showing the manner of laying off the reciprocal of a 1.618 rectangle.

Referring to the drawings, the numeral 10 designates a carrying member which preferably consists of a rectangular strip of sheetlike material such as cardboard or celluloid.

Fig. 1 shows the methodof obtaining what be referred to as a mean and extreme ratio rectangle. On the line LB, a distance LT is laid off from L equal to LA and on the line BC a distance BU is laid off from B equal to BT. Through the point U a line -UV is drawn parallel. to the baseline BA and a rectangle ABUV is produced in which.

from the rule relating to mean and extreme ratios, we know that the length of the line UV is 1.618 when the line VA is taken as 1. This rectangle may be referred to as a1.618 rectangle, the reciprocal of which is .618. In Fig. 3, a 1.618 rectangle ABUV has been drawn in the square ABCDendfthe diagonal BV is extended to meet the extended line CD at the point Z. From the point Z a line ZY parallel to VA is drawn to meetthe extended line BA- at Y. We then have two right angle triangles ADY and AUV which -we have the following proportion are equalto each other since the 'angles are equal and AD equals UV. Hence AY and VA are equal. The line'AX may be readily drawn parallel to the line BZ and from X the line Xl/V is, drawn parallel to AY. We 8 therefore have rectangle AWXY from' wh ch. by comparison with therectangle ABUV'we have the following proportion:-

uvivanan rr Substituting the known quantities in this proportion, We have 1.618 1 :XY or r. 1.618 In the rectangle ADZY, itwill be seen that we have a square WDZX and the reciprocal of a 1:618 rectangleplaced side by side. Re-

. ferring tothe same figure, the diagonal AU is continued untilit meets the extended lme CD at the point Z and-the line ZY isdrawn parallel to the line BC to meet the extended line AB, at the point Y. Since the right angle triangles AUV and AZ. D are similar, I

v UVzVAnDZzDA V The rectangle ADZ'Y therefore has the same proportion as the'rectangle ABUV and is a 1.618 rectangle and the equal.rectangle BCZY isganother 1.618 rectangle. The rectangles BCZY and ADZY are the reciprocals and hence DZ and CZ? have'au-value of .618. .Hence in the rectangle ZZYY the side ZZ is .618plus 1 plus .618 which equals 2.236,.which is equal to I a x and thisrectangle is aroot 5 rectangle since ZY;1., In this figure,.we have two 1.618 rectanglesBGZY and ADZY with their squares superimposed from which it is observed that it is unnecessary to proceed'f'urtherin the. series than the root 5rectangle.

2 a plan view showing thecarrying inconmen er. upon which the lines and rectangles previously determined have been drawn. It is obvious that the carrying member may be usedfor laying out rectangles proportional to. those indicated thereon by trauma point B and cai'rbe made to pass through any: one of the points on either of the two squares.

' 'One manner of using the device willbe un derstood from Fi 3' assuming that af-12618 rectangle is to be drawn adjacent the right hand portion of the rectangle ABCD. "The arm 12 01- the device is turned on its pivot 13 so that the straight edge 14 passes through the point V indicated iu'Figj. 1. The device thus set is placed with the pivot 13 directly over the point B and with the base line AB of the device directly over the line AB of the rectangle. This, of coursecanhe readily done whenthe device is constructed of transparent celluloid. The point where the straight edge l lcrosses the line GD extended is'marked at-Z, and'upon completing the rectangle" ADZY,-it *wiil be found to be a 1.618 rectangle. root'2 rectangle may be similarly drawn' by placing the straight edge 14 so as to extend through the point F, a root 3 rectangle maybe similarly drawn .by placing the straight edge so as to extend through the one of said points which 001'- responds to the desired rectangle.

2. An instrument for obtaining dynamically symmetrical ratios comprising a rec-- tangular slfeet having two equal squares marked thereon with one side in common, an armpivotedto-said sheet: common corner of said squares, said arm having a straight ed e which is directed through the pivotal pointj for; allf: positions the arm 3 around the pivotal;w point; andpredetermined indicating points located at intervals along those v sidesiof said -squares which are remote from v the pivotal point, said indicating points he "ingsol disposed itliat root rectangles and a 1.618 rectangle may 'be-laid out .by'drawing' lines along: said straight edgefwhen said straight edge passes throughthe one ofisaid points which corresponds to the desiredrectangle.

In testimony whereof I liereiinto aflix my signature.

roan ROBBINS.

through the point K, a root 4 rectangle may be similarly drawn by placing the straight edge so as to extend through the point L, while a root 5 rectangle may be similarly drawn by placing the straight edge so as to extend through the point M. Inorderto draw a 1.618 rectangle adjacent the-left hand POItiOIl'Qf the rectangleABGD, the straight edge 14 is placed. sov as to extend through the left handipoint corresponding to-the point V and the pivot 13 is then placed directly over the point'A. Theaprocedure previously set forth is repeated to determine therectangle BGZY. The root rectangles above referred to may also belaid' out at the left in similarmanner.

I claim: j

1. Anfiinstrument 'for obtainingdy-iiamically symmetrical ratios-comprising a. "rectangular sheet having two equal squares marked thereon with one side in common, an arm pivoted to said sheet at. a common cornerof said squares, said arm having a straight edge which is directed "through the pivotal point for all positions'ot the-arm around the pivotal point, and predetermined indicating'points located at intervals along those sides of said squares which are remote from the pivotal point, said indicating points being so disposed that root rectangles may be laid out by drawing lines along said 05 straight edge whensaid straight edge passes iio 

